Why Lutherans insist of being called Lutheran

Martin Luther: On Receiving Both Kinds in the Sacrament (1522)

Finally, I see that I must add a good word of admonition to those whom Satan has now begun to persecute. For there are some among them who think that when they are attacked they can escape the danger by saying: I do not hold with Luther or with anyone else, but only with the holy gospel and the holy church, or with the Roman church. For saying so they think they will be left in peace. Yet in their hearts they regard my teaching as the teaching of the gospel and stand by it. In reality this kind of statement does not help them, and it is in effect a denial of Christ. Therefore, I beg such people to be very careful.

True, by any consideration of body or soul you should never say: I am Lutheran, or Papist. For neither of them died for you, or is your master. Christ alone died for you, he alone is your master, and you should confess yourself a Christian. But if you are convinced that Luther’s teaching is in accord with the gospel and that the pope’s is not, then you should not discard Luther so completely, lest with him you discard also his teaching, which you nevertheless recognize as Christ’s teaching. You should rather say: Whether Luther is a rascal or a saint I do not care; his teaching is not his, but Christ’s. 

For you will observe that the tyrants are not out merely to destroy Luther, but to wipe out the teaching. It is on account of the teaching that they attack you and ask you whether you are Lutheran. Here you must be sure not to speak with slippery or evasive words but frankly to confess Christ, no matter who did the preaching—Luther, or Tom, Dick, or Harry. 

The person you can forget; but the teaching you must confess. Paul also writes thus to Timothy in 2 Tim. 1[:8]: “Do not be ashamed then of testifying to our Lord, nor of me, a prisoner for his sake.” If it had been enough here for Timothy to confess the gospel, Paul would not have commanded him not to be ashamed also of Paul—not of Paul as a person but of Paul as a prisoner for the sake of the gospel. Now if Timothy had said, I do not hold with Paul or with Peter, but with Christ, when he knew that Peter and Paul were teaching Christ, then he would actually thereby have denied Christ himself. For Christ says in Matt. 10 concerning those who preach him: “He who receives you receives me, and he who rejects you rejects me.” Why this? Because holding thus with his messengers, those who bring his word, is the same as holding with Christ himself and with his word. (LW 36:266)